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Search: id:A093101
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| A093101 |
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Cancellation factor in reducing Sum_{k=0...n} 1/k! to lowest terms. |
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18
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| 1, 1, 1, 2, 1, 2, 1, 20, 1, 10, 1, 8, 5, 2, 5, 4, 1, 130, 1, 4000, 1, 2, 5, 52, 5, 494, 1, 40, 1, 10, 13, 4, 25, 38, 5, 16, 13, 230, 13, 20, 1, 46, 5, 104, 475, 62, 1, 20, 1, 130, 31, 832, 2755, 74, 5, 4, 13, 50, 1, 40, 23, 2, 2795, 76, 34385, 2, 1, 80, 1, 650, 1, 2812, 5, 74, 5
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Same as n!/A061355(n) and (1+n+n(n-1)+n(n-1)(n-2)+...+n!)/A061354(n). Relatively prime to n.
GCD(a(n),a(n+1)) = 1.
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REFERENCES
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J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, Amer. Math. Monthly 113 (2006) 637-641.
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LINKS
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J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality
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FORMULA
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GCD(n!, 1+n+n(n-1)+n(n-1)(n-2)+...+n!)
GCD(n!, A(n)) where A(0) = 1, A(n) = n*A(n-1)+1
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EXAMPLE
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E.g. 1/0!+1/1!+1/2!+1/3!=16/6=(2*8)/(2*3) so a(3)=2.
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MATHEMATICA
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f[n_] := n! / Denominator[ Sum[1/k!, {k, 0, n}]]; Table[ f[n], {n, 0, 74}] (from Robert G. Wilson v)
(A[n_] := If[n==0, 1, n*A[n-1]+1]; Table[GCD[A[n], n! ], {n, 0, 74}])
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CROSSREFS
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Cf. A093647, A093651.
(n+1)!/(a(n)*a(n+1)) = A123899(n). (n+3)!/(a(n)*a(n+1)*a(n+2)) = A123900(n). (n+3)/GCD(a(n), a(n+2)) = A123901(n). Cf. also A000522, A061354, A061355.
Sequence in context: A134304 A134569 A072883 this_sequence A082469 A088151 A024375
Adjacent sequences: A093098 A093099 A093100 this_sequence A093102 A093103 A093104
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KEYWORD
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nonn
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AUTHOR
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Jonathan Sondow (jsondow(AT)alumni.princeton.edu), May 10 2004, Oct 18 2006
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), May 14 2004
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